Early Warning Signals for Critical Transitions: A Generalized Modeling Approach

Critical transitions are sudden, often irreversible, changes that can occur in a large variety of complex systems; signals that warn of critical transitions are therefore highly desirable. We propose a new method for early warning signals that integrates multiple sources of information and data about the system through the framework of a generalized model. We demonstrate our proposed approach through several examples, including a previously published fisheries model. We regard our method as complementary to existing early warning signals, taking an approach of intermediate complexity between model-free approaches and fully parameterized simulations. One potential advantage of our approach is that, under appropriate conditions, it may reduce the amount of time series data required for a robust early warning signal.

[1]  William A. Brock,et al.  Tipping points, abrupt opinion changes, and punctuated policy change , 2003 .

[2]  C. Kuehn A mathematical framework for critical transitions: Bifurcations, fast–slow systems and stochastic dynamics , 2011, 1101.2899.

[3]  Monica G. Turner,et al.  Ecological Thresholds: The Key to Successful Environmental Management or an Important Concept with No Practical Application? , 2006, Ecosystems.

[4]  M. Scheffer,et al.  Regime shifts in marine ecosystems: detection, prediction and management. , 2008, Trends in ecology & evolution.

[5]  J. Anderies,et al.  Grazing Management, Resilience, and the Dynamics of a Fire-driven Rangeland System , 2002, Ecosystems.

[6]  A. Hastings,et al.  Thresholds and the resilience of Caribbean coral reefs , 2007, Nature.

[7]  M. Rosenzweig Paradox of Enrichment: Destabilization of Exploitation Ecosystems in Ecological Time , 1971, Science.

[8]  Martin Zumsande,et al.  Extension of Generalized Modeling and Application to Problems from Cell Biology , 2011 .

[9]  V. Guttal,et al.  Changing skewness: an early warning signal of regime shifts in ecosystems. , 2008, Ecology letters.

[10]  Carl J. Walters,et al.  Cultivation/depensation effects on juvenile survival and recruitment: implications for the theory of fishing , 2001 .

[11]  Thilo Gross,et al.  Generalized Models Reveal Stabilizing Factors in Food Webs , 2009, Science.

[12]  Wolfgang Lucht,et al.  Tipping elements in the Earth's climate system , 2008, Proceedings of the National Academy of Sciences.

[13]  C. Wissel A universal law of the characteristic return time near thresholds , 1984, Oecologia.

[14]  L. Ross,et al.  Environmental policy in China , 1988 .

[15]  S. Carpenter,et al.  Turning back from the brink: Detecting an impending regime shift in time to avert it , 2009, Proceedings of the National Academy of Sciences.

[16]  S. Carpenter,et al.  Leading indicators of trophic cascades. , 2007, Ecology letters.

[17]  Berkeley,et al.  Critical transitions in nature and society , 2009, Choice Reviews Online.

[18]  J. Steele Regime shifts in the ocean: reconciling observations and theory [review article] , 2004 .

[19]  Thilo Gross,et al.  Long food chains are in general chaotic , 2005 .

[20]  S. Carpenter,et al.  Rising variance: a leading indicator of ecological transition. , 2006, Ecology letters.

[21]  Ludek Berec,et al.  Single-species models of the Allee effect: extinction boundaries, sex ratios and mate encounters. , 2002, Journal of theoretical biology.

[22]  George Sugihara,et al.  Ecology for bankers , 2008 .

[23]  Thilo Gross,et al.  Generalized models as a universal approach to the analysis of nonlinear dynamical systems. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[24]  Thilo Gross,et al.  Nonlocal generalized models of predator-prey systems , 2011, 1105.3662.

[25]  S. Carpenter,et al.  Early Warnings of Regime Shifts: A Whole-Ecosystem Experiment , 2011, Science.

[26]  J Swanson,et al.  Business Dynamics—Systems Thinking and Modeling for a Complex World , 2002, J. Oper. Res. Soc..

[27]  S. Carpenter,et al.  Early-warning signals for critical transitions , 2009, Nature.

[28]  Tilo Winkler,et al.  Self-organized patchiness in asthma as a prelude to catastrophic shifts , 2005, Nature.

[29]  Thilo Gross,et al.  Generalized modeling of ecological population dynamics , 2010, Theoretical Ecology.

[30]  Marten Scheffer,et al.  Regime Shifts in the Sahara and Sahel: Interactions between Ecological and Climatic Systems in Northern Africa , 2003, Ecosystems.

[31]  Steven J. D. Martell,et al.  Fisheries Ecology and Management , 2004 .

[32]  Brian Dennis,et al.  The evidence for Allee effects , 2009, Population Ecology.

[33]  S. Carpenter,et al.  Interacting regime shifts in ecosystems: implication for early warnings , 2010 .

[34]  C. S. Holling,et al.  Regime Shifts, Resilience, and Biodiversity in Ecosystem Management , 2004 .

[35]  Robert H. Nelson,et al.  Punctuated Equilibrium and the Dynamics of U.S. Environmental Policy , 2008 .

[36]  M. Scheffer,et al.  Slowing down as an early warning signal for abrupt climate change , 2008, Proceedings of the National Academy of Sciences.

[37]  Marten Scheffer,et al.  Spatial correlation as leading indicator of catastrophic shifts , 2010, Theoretical Ecology.

[38]  S. Carpenter,et al.  Catastrophic shifts in ecosystems , 2001, Nature.

[39]  J. A. Kuznecov Elements of applied bifurcation theory , 1998 .